ORIE 3500/5500 – Engineering Probability and Statistics II
Fall 2010
Assignment 1
Problem 1
We toss a coin 3 times. For this experiment we choose
the sample space
Ω =
HHH, THH, HTH, HHT, TTH, THT, HTT, TTT
,
where
T
stands for tails and
H
stands for heads.
a.
Write down the outcomes comprising the following events:
A
:
“we throw tails exactly twice”;
B
:
“we throw tails at least twice”;
C
:
“tails did not appear
before
a head appeared”;
D
:
“the first throw results in tails”
.
b.
Write down the outcomes comprising the following events:
A
c
,
A
∪
(
C
∩
D
),
A
∩
D
c
.
Problem 2
For events
A
and
B
, it is known that
P
(
A
) =
.
6
, P
(
B
) =
.
7 but
P
(
A
∩
B
) is unknown. What are the smallest and the largest
value that
P
(
A
∩
B
) may take?
Problem 3
A town has 4 plumbers. If 4 houses have plumbing
problems on a given day, what is the probability that exactly
i
plumbers
are called, for
i
= 1
,
2
,
3
,
4. Explain what assumptions, if any, you are
making.
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 Fall '09
 SAMORODNITSKY
 Probability, Card game, following events

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